Submodular maximization subject to a p-matchoid constraint has various applications in machine learning, particularly in tasks such as feature selection, video and text summarization, movie recommendation, graph-based learning, and constraintbased optimization. We study this problem in the dynamic setting, where a sequence of insertions and deletions of elements to a p-matchoid M(V,I) occurs over time and the goal is to efficiently maintain an approximate solution. We propose a dynamic algorithm for non-monotone submodular maximization under a p-matchoid constraint. For a p-matchoid M(V,I) of rank k, defined by a collection of m matroids, our algorithm guarantees a (2p +2 p p(p +1) +1 +ϵ)-approximate solution at any time t in the update sequence, with an expected amortized query complexity of O(ϵ 3 pk4 log2(k)) per update.

Generative models of graphs based on discrete Denoising Diffusion Probabilistic Models (DDPMs) offer a principled approach to molecular generation by systematically removing structural noise through iterative atom and bond adjustments. However, existing formulations are fundamentally limited by their inability to adapt the graph size (that is, the number of atoms) during the diffusion process, severely restricting their effectiveness in conditional generation scenarios such as property-driven molecular design, where the targeted property often correlates with the molecular size. In this paper, we reformulate the noising and denoising processes to support monotonic insertion and deletion of nodes. The resulting model, which we call GRIDDD, dynamically grows or shrinks the chemical graph during generation. GRIDDD matches or exceeds the performance of existing graph Diffusion Models on molecular property targeting despite being trained on a more difficult problem. Furthermore, when applied to molecular optimization, GRIDDD exhibits competitive performance compared to specialized optimization models. This work paves the way for size-adaptive molecular generation with graph diffusion.

Binary data factorization is common, but real-valued methods ignore discreteness and yield hard-to-interpret factors. Boolean Matrix Factorization (BooMF) instead decomposes a binary matrix into two lower-rank binary matrices via logical AND and OR, expressing the data as a Boolean disjunction of interpretable patterns. In cancer genomics, BooMF can reveal coordinated feature changes that may drive tumor evolution, unlike rotational or additive decompositions. Most existing BooMF methods are heuristic, greedy, sensitive to initialization, prone to local optima, and do not support principled model selection or uncertainty quantification. We introduce Bayesian Boolean Matrix Factorization (BBMF), a fully conjugate generative model with sparsity-inducing priors. It enforces Boolean constraints, yields interpretable latent factors with coherent uncertainty quantification, and admits Gibbs sampling with closed-form full conditionals. Because cancer evolution often involves widespread, near-simultaneous chromosome-number changes (e.g., whole-genome duplication followed by instability and selection), Boolean factorizations capture these patterns more naturally than additive models. Applied to arm-level copy-number alteration data in multiple myeloma, where entries indicate presence/absence of chromosomal-arm amplifications, BBMF finds a small set of interpretable bicliques linking patient subsets to recurrently co-altered chromosomal arms, providing a compact, biologically meaningful summary of tumor heterogeneity and demonstrating BBMF's utility for uncovering discrete latent structure in complex binary data.

Recent provably secure linguistic steganography (PSLS) methods rely on mainstream autoregressive language models (ARMs) to address historically challenging tasks, that is, to disguise covert communication as "innocuous" natural language communication. However, due to the characteristic of sequential generation of ARMs, the stegotext generated by ARM-based PSLS methods will produce serious error propagation once it changes, making existing methods unavailable under an active tampering attack. To address this, we propose a robust provably secure linguistic steganography with diffusion language models (DLMs). Unlike ARMs, DLMs can generate text in partial parallel manner, allowing us to find robust positions for steganographic embedding that can be combined with error-correcting codes. Furthermore, we introduce an error correction strategies, including pseudorandom error correction and neighborhood search correction, during steganographic extraction. Theoretical proof and experimental results demonstrate that our method is secure and robust. It can resist token ambiguity in stegotext segmentation and, to some extent, withstand token-level attacks of insertion, deletion, and substitution.

Data duplication within large-scale corpora often impedes large language models' (LLMs) performance and privacy. In privacy-concerned federated learning scenarios, conventional deduplication methods typically rely on trusted third parties to perform uniform deletion, risking loss of informative samples while introducing privacy vulnerabilities. To address these gaps, we propose Federated ReWeighting (FedRW), the first privacy-preserving framework, to the best of our knowledge, that performs soft deduplication via sample reweighting instead of deletion in federated LLM training, without assuming a trusted third party. At its core, FedRW proposes a secure, frequency-aware reweighting protocol through secure multi-party computation, coupled with a parallel orchestration strategy to ensure efficiency and scalability. During training, FedRW utilizes an adaptive reweighting mechanism with global sample frequencies to adjust individual loss contributions, effectively improving generalization and robustness. Empirical results demonstrate that FedRW outperforms the state-of-the-art method by achieving up to $28.78\times$ speedup in preprocessing and approximately $11.42$\% improvement in perplexity, while offering enhanced security guarantees. FedRW thus establishes a new paradigm for managing duplication in federated LLM training.

Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

We argue that current definitions of machine unlearning are underspecified for second-order optimizers. We compare first-order and second-order learners for their ability to handle the data deletion task with varying degrees of eigendecomposition to mimic the loss model memory. While both first and second-order methods realign with the ideal counterfactul in terms of performance and gradient, the second-order optimizer shows significant volatility in the optimizer state. This indicates residual information, supposedly deleted, that isn't detectable by first-order analysis. Various eigendecay treatments show that stability and information loss is regained only under controlled state pertubation where geometric information (or memory) is erased.

Given a point set P M from a metric space (M,d)and numbers k,z N, the metric k-center problem with z outliers is to find a set C P of k points such that the maximum distance of all but at most z outlier points of P to their nearest center in C is minimized. We consider this problem in the fully dynamic model, i.e., under insertions and deletions of points, for the case that the metric space has a bounded doubling dimension dim. We utilize a hierarchical data structure to maintain the points and their neighborhoods, which enables us to efficiently find the clusters. In particular, our data structure can be queried at any time to generate a (3 + ε)-approximate solution for input values of k and z in worst-case query time ε O(dim)klognloglog, where is the ratio between the maximum and minimum distance between two points in P. Moreover, it allows insertion/deletion of a point in worst-case update time ε O(dim) lognlog . Our result achieves a significantly faster query time with respect to k and z than the current state-of-theart by Pellizzoni, Pietracaprina, and Pucci [18], which uses ε O(dim)(k+z)2 log query time to obtain a (3+ε)-approximate solution.

In this part, we state the orthogonal decomposition Property, motivate its importance with a pedagogical example, and finally prove Proposition 1, which enables the decomposition property in the context of HSIC attribution method. A.1 Orthogonal Decomposition Property Let x = {x1,..., xn}2Xn be a set of n univariate random input variables. For any subset A = {l1,...,l |A|} { 1,...,n}, we denote xA =( xl1,..., xl|A|) the vector of input variables with indices in A. Let y the random output variable defined by y = f(x), F the RKHS defined by the kernel kA: X|A|! R and G the RKHS defined by the kernel l: Y! R. In [11], the author shows that for any choice of kernel l, if we respect some constraints on the kernel kA, we can construct indices HSIC (xA,y) that satisfy the following decomposition property. The constraints on the kernel kA are detailed in the main document and in the last section of this appendix.

Privacy is a central challenge for systems that learn from sensitive data sets, especially when a system's outputs must be continuously updated to reflect changing data. We consider the achievable error for differentially private continual release of a basic statistic--the number of distinct items--in a stream where items may be both inserted and deleted (the turnstile model). With only insertions, existing algorithms have additive error just polylogarithmic in the length of the stream T. We uncover a much richer landscape in the turnstile model, even without considering memory restrictions. We show that every differentially private mechanism that handles insertions and deletions has worst-case additive error at least T1/4 even under a relatively weak, event-level privacy definition. Then, we identify a parameter of the input stream, its maximum flippancy, that is low for natural data streams and for which we give tight parameterized error guarantees. Specifically, the maximum flippancy is the largest number of times that the contribution of a single item to the distinct elements count changes over the course of the stream. We present an item-level differentially private mechanism that, for all turnstile streams with maximum flippancy w, continually outputs the number of distinct elements with an O( p w polylogT) additive error, without requiring prior knowledge of w. We prove that this is the best achievable error bound that depends only on w, for a large range of values of w. When w is small, the error of our mechanism is similar to the polylogarithmic in T error in the insertion-only setting, bypassing the hardness in the turnstile model.